Chapter Eight

Chapter EightGases, Liquids, and Solids

Fundamentals of General, Organic, and Biological Chemistry

5th Edition

James E. Mayhugh

Oklahoma City University

2007 Prentice Hall, Inc.

Prentice Hall © 2007 Chapter Eight 2

Outline

► 8.1 States of Matter and Their Changes► 8.2 Gases and the Kinetic–Molecular Theory► 8.3 Pressure► 8.4 Boyle’s Law: The Relation Between Volume and Pressure► 8.5 Charles’s Law: The Relation Between Volume and Temperature► 8.6 Gay-Lussac’s Law: The Relation Between Pressure and Temperature► 8.7 The Combined Gas Law► 8.8 Avogadro’s Law: The Relation Between Volume and Molar Amount► 8.9 The Ideal Gas Law► 8.10 Partial Pressure and Dalton’s Law► 8.11 Intermolecular Forces► 8.12 Liquids► 8.13 Water: A Unique Liquid► 8.14 Solids► 8.15 Changes of State


8.1 States of Matter and Their Changes

► Matter exists in any of three phases, or states—solid, liquid, and gas, depending on the attractive forces between particles, temperature, and pressure.

► In a gas, the attractive forces between particles are very weak compared to their kinetic energy, so the particles move about freely, are far apart, and have almost no influence on one another.

► In a liquid, the attractive forces between particles are stronger, pulling the particles close together but still allowing them considerable freedom to move about.


In a solid, the attractive forces are much stronger than the kinetic energy of the particles, so the atoms, molecules, or ions are held in a specific arrangement and can only wiggle around in place.


►Phase change or change of state: The transformation of a substance from one state to another.

►Melting point (mp): The temperature at which solid and liquid are in equilibrium.

►Boiling point (bp): The temperature at which liquid and gas are in equilibrium.

►Sublimation: A process in which a solid changes directly to a gas.

►Melting, boiling, and sublimation all have H > 0, and S > 0. This means they are nonspontaneous below and spontaneous above a certain temperature.



8.2 Gases and the Kinetic-Molecular Theory

► The behavior of gases can be explained by a group of assumptions known as the kinetic–molecular theory of gases. The following assumptions account for the observable properties of gases:

► A gas consists of many particles, either atoms or molecules, moving about at random with no attractive forces between them. Because of this random motion, different gases mix together quickly.


► The amount of space occupied by the gas particles themselves is much smaller than the amount of space between particles. Most of the volume taken up by gases is empty space, accounting for the ease of compression and low densities of gases.

► The average kinetic energy of gas particles is proportional to the Kelvin temperature. Thus, gas particles have more kinetic energy and move faster as the temperature increases. (In fact, gas particles move much faster than you might suspect. The average speed of a helium atom at room temperature and atmospheric pressure is approximately 1.36 km/s, or 3000 mi/hr, nearly that of a rifle bullet.)


► Collisions of gas particles, either with other particles or with the wall of their container, are elastic; that is, the total kinetic energy of the particles is constant. The pressure of a gas against the walls of its container is the result of collisions of the gas particles with the walls. The number and force of collisions determines the pressure.

► A gas that obeys all the assumptions of the kinetic–molecular theory is called an ideal gas. All gases behave somewhat differently than predicted by the kinetic–molecular theory at very high pressures or very low temperatures. Most real gases display nearly ideal behavior under normal conditions.


8.3 Pressure

► Pressure (P) is defined as a force (F) per unit area (A) pushing against a surface; P = F/A.

► A barometer measures pressure as the height of a mercury column. Atmospheric pressure presses down on mercury in a dish and pushes it up a tube.

► Pressure units:

1 atm = 760 mm Hg = 14.7 psi = 101,325 Pa

1 mm Hg = 1 torr = 133.32 Pa


Gas pressure inside a container is often measured using an open-end manometer, a simple instrument similar in principle to the mercury barometer.


8.4 Boyle’s Law: The Relation Between Volume and Pressure

► Boyle’s law: The volume of a gas is inversely proportional to its pressure for a fixed amount of gas at a constant temperature. That is, P times V is constant when the amount of gas n and the temperature T are kept constant.

► V 1/P or PV = k if n and T are constant

► If: P1V1 = k and P2V2 = k

► Then: P1V1 = P2V2


The volume of a gas decreases proportionately as its pressure increases. If the pressure of a gas sample is doubled, the volume is halved.


Graph (a) demonstrates the decrease in volume as pressure increases, whereas graph (b) shows the linear relationship between V and 1/P.

Problem 8.41

►The volume of a balloon is 2.85 L at 1.00 atm. What pressure is required to compress the balloon to a volume of 1.70 L?

Use Boyle’s Law:

P1V1 = P2V2 now, solve for P2

divide both sides by V2

P1V1/V2 = P2


P2 = P1V1/V2

P2 = (1.00 atm)(2.85 L)/(1.70 L)

= 1.68 atm



8.5 Charles’ Law: The Relation Between Volume and Temperature

► Charles’s law: The volume of a gas is directly proportional to its Kelvin temperature for a fixed amount of gas at a constant pressure. That is, V divided by T is constant when n and P are held constant.

► V T or V/T = k if n and P are constant

► If: V1/T1 = k and V2/T2 = k

► Then: V1/T1 = V2/T2


If the Kelvin temperature of a gas is doubled, its volume doubles.


As the temperature goes up, the volume also goes up.

Problem 8.47

►A hot air balloon has a volume of 875 L. What is the original temperature of the balloon if its volume changes to 955 L when heated to 56oC?

Charles’ Law:

V1/T1 = V2/T2 now, solve for T1

divide both sides by V1

1/T1 = V2/V1T2

take reciprocal of both sides

T1 = V1T2/V2


Make sure to use Kelvin degrees

T1 = V1T2/V2

T2 = 56oC + 273 = 329 K

T1 = (875 L)(329K)/(955 L)

= 301K convert to oC (subtract 273)

28oC



8.6 Gay-Lussac’s Law: The Relation Between Pressure and Temperature

► Gay-Lussac’s law: The pressure of a gas is directly proportional to its Kelvin temperature for a fixed amount of gas at a constant volume. That is, P divided by T is constant when n and V are held constant.

► P T or P/T = k if n and V are constant

► If: P1/T1 = k and P2/T2 = k

► Then: P1/T1 = P2/T2


As the temperature goes up, the pressure also goes up.

Problem 8.52

►An aerosol can has an internal pressure of 3.85 atm at 25oC. What temperature is required to raise the pressure to 18.0 atm?

►Use Gay-Lussac’s law

P1/T1 = P2/T2 Now, solve for unknown variable.divide both sides by P2

P1/T1P2 = 1/T2

take reciprocal of both sides

T2 = T1P2/P1


T2 = T1P2/P1

T1 = 25oC + 273

= 298 K

T2 = (298 K)(18.0 atm)/(3.85 atm)

= 1390 K (1117 oC)



8.7 The Combined Gas Law

► Since PV, V/T, and P/T all have constant values for a fixed amount of gas, these relationships can be merged into a combined gas law for a fixed amount of gas.

► Combined gas law: PV/T = k if n constant

►P1V1/T1 = P2V2/T2

► If any five of the six quantities in this equation are known, the sixth can be calculated.

► See problems 8.8, 9, 54, 57, 60


8.8 Avogadro’s Law: The Relation Between Volume and Molar Amount

► Avogadro’s law: The volume of a gas is directly proportional to its molar amount at a constant pressure and temperature. That is, V divided by n is constant when P and T are held constant.

► V n or V/n = k if P and T are constant

► If: V1/n1 = k and V2/n2 = k

► Then: V1/n1 = V2/n2


► The molar amounts of any two gases with the same volume are the same at a given T and P.

► Standard temperature and pressure:(STP) = 0C (273.15 K) and 1 atm (760 mm Hg)

► Standard molar volume of a gas at STP = 22.4 L/mol

Problem 8.72

►What is the mass of CH4 in a sample that occupies a volume of 16.5 L at STP?

1 mol of any gas at STP = 22.4 L

16.5 L x 1 mol/22.4 L x 16.0 g CH4/1 mol CH4

= 11.8 g CH4


Density of gases g/L

Density of Helium:

1 mol/22.4 L x 4.00g He/mol He = 0.178 g/L

Density of Nitrogen:

1 mol/22.4 L x 28.0g N2/mol N2 = 1.25 g/L

Density of a gas is proportional to its Mol. Wt.

So… H2 < He < CH4 < CO = N2 < CO2



8.9 The Ideal Gas Law

► Ideal gas law: The relationships among the four variables P, V, T, and n for gases can be combined into a single expression called the ideal gas law.

► PV/nT = R (a constant value) or PV = nRT► If the values of three of the four variables in the

ideal gas law are known, the fourth can be calculated.

► Values of the gas constant R:For P in atm: R = 0.0821 L·atm/mol·KFor P in mm Hg: R = 62.4 L·mm Hg/mol·K

Problem 8.11

►An aerosol spray can of deodorant with a volume of 350 mL contains 3.2 g of propane gas (C3H8) as a propellant. What is the pressure in the can at 20oC?

PV = nRT solve for P

P = nRT/V


Convert units

P = nRT/V

R = 0.0821 L.atm/mol.K

n = moles propane (C3H8)

= 3.2 g C3H8 x 1 mol C3H8/ 44 g C3H8

= 0.073 mol

T = K degrees = 20oC + 273

= 293 K

V = Liters = 350 mL x 1 L/1000 mL

= 0.350 L


Now Solve for P

P = nRT/V n R T / V

= (0.073 mol)(0.0821 L.atm/mol.K)(293 K)/0.350 L

= 5.0 atm




8.10 Partial Pressure and Dalton’s law

► Dalton’s law: The total pressure exerted by a gas mixture of (Ptotal) is the sum of the partial pressures of the components in the mixture.

► Dalton’s law Ptotal = Pgas1 + Pgas2 + Pgas3 + …

► Partial pressure: The contribution of a given gas in a mixture to the total pressure.

Dry Air at Sea Level

►Pressure at sea level is 760 mm Hg (1 atm)►Percent composition of dry air is:

78% N2 (78% of the pressure is caused by N2)

21% O2 (21% of the pressure is caused by O2)

1% Ar (1% of the pressure is caused by Ar)

Ptotal = PN2 + PO2

+ PAr

= (0.78)(760) + (0.21)(760) + (0.01)(760)

760 = 593 mm + 160 mm + 7 mm


Problem 8.14

►Deep sea divers breathe a mixture of 98% He and

2% O2 at 9.50 atm of pressure. How does the partial pressure of O2 in diving gas compare with its partial pressure in normal air?

Normal air is 21% O2

PPO2 in air: (0.21 O2)(760 mm Hg) = 160 mm Hg

Tank pressure is 9.50 atm x 760 mm Hg/1 atm =

7220 mm Hg

PPO2 in tank = (0.02)(7220) = 144 mm Hg



8.11 Intermolecular Forces in Liquids

► Intermolecular force: A force that acts between molecules and holds molecules close to one another. There are three major types of intermolecular forces.

► Dipole–dipole forces are weak, with strengths on the order of 1 kcal/mol

► London dispersion forces are weak, in the range 0.5–2.5 kcal/mol. They increase with molecular weight and molecular surface area.

► Hydrogen bonds can be quite strong, with energies up to 10 kcal/mol.

Prentice Hall © 2007 Chapter Five 40

5.8 Polar Covalent Bonds and Electronegativity

► Electrons in a covalent bond occupy the region between the bonded atoms.

► If the atoms are identical, as in H2 and Cl2, electrons are attracted equally to both atoms and are shared equally.

► If the atoms are not identical, however, as in HCl, the bonding electrons may be attracted more strongly by one atom than by the other and thus shared unequally. Such bonds are known as polar covalent bonds.


When charges separate in a neutral molecule, the molecule has a dipole moment and is said to be polar.


►In HCl, electrons spend more time near the chlorine than the hydrogen. Although the molecule is overall neutral, the chlorine is more negative than the hydrogen, resulting in partial charges on the atoms.

►Partial charges are represented by a - on the more negative atom and + on the more positive atom.

►The ability of an atom to attract electrons is called the atom’s electronegativity.

►Fluorine, the most electronegative element, assigned a value of 4, and less electronegative atoms assigned lower values.


Elements at the top right of the periodic table are most electronegative, those at the lower left are least electronegative. Noble gases are not assigned values.


►As a rule of thumb, electronegativity differences of less than 0.5 result in nonpolar covalent bonds, differences up to 1.9 indicate increasingly polar covalent bonds, and differences of 2 or more indicate ionic bonds.

►There is no sharp dividing line between covalent and ionic bonds; most bonds fall somewhere in-between.


5.9 Polar Molecules

►Entire molecules can be polar if electrons are attracted more strongly to one part of the molecule than to another.

►Molecules polarity is due to the sum of all individual bond polarities and lone-pair contribution in the molecule.

►Polarity has a dramatic effect on the physical properties of molecules, particularly on melting points, boiling points, and solubility.


► Dipoles or polarity can be represented by an arrow pointing to the negative end of the molecule with a cross at the positive end resembling a + sign.


►Just because a molecule has polar covalent bonds does not mean that the molecule is polar overall.

►Carbon dioxide and tetrachloromethane molecules have no net polarity because their symmetrical shapes cause the individual bond polarities to cancel each other out.


Dipole–dipole forces: The positive and negative ends of polar molecules are attracted to one another by dipole–dipole forces. As a result, polar molecules have higher boiling points than nonpolar molecules of similar size.


►Only polar molecules experience dipole–dipole forces, but all molecules, regardless of structure, experience London dispersion forces.

►(a) On average, the electron distribution in a nonpolar molecule is symmetrical. (b) At any instant, it may be unsymmetrical, resulting in a temporary polarity that can attract neighboring molecules.


A hydrogen bond is an attractive interaction between an unshared electron pair on an electronegative O, N, or F atom and a positively polarized hydrogen atom bonded to another electronegative O, N, or F. Hydrogen bonds occur in both water and ammonia.


The boiling points of NH3, H2O, and HF are much higher than the boiling points of their second row neighbor CH4 and of related third-row compounds due to hydrogen bonding.


8.12 Liquids

► Molecules are in constant motion in the liquid state. If a molecule happens to be near the surface of a liquid, and if it has enough energy, it can break free of the liquid and escape into a state called vapor.

► Once molecules have escaped from the liquid into the gas state, they are subject to all the gas laws. The gas molecules make their own contribution to the total pressure of the gas above the liquid according to Dalton’s law. We call this contribution the vapor pressure of the liquid.


► Vapor pressure rises with increasing temperature until ultimately it becomes equal to the pressure of the atmosphere. At this point, bubbles of vapor form under the surface and force their way to the top; this is called boiling.

► At a pressure of exactly 760 mm Hg, boiling occurs at what is called the normal boiling point.

► If atmospheric pressure is higher or lower than normal, the boiling point of a liquid changes accordingly. At high altitudes, for example, atmospheric pressure is lower than at sea level, and boiling points are also lower.


At a liquid’s boiling point, its vapor pressure is equal to atmospheric pressure. Commonly reported boiling points are those at 760 mm Hg.


8.13 Water: A Unique Liquid

► Water covers nearly 71% of the Earth’s surface, it accounts for 66% of the mass of an adult human body, and it is needed by all living things.

► Water has the highest specific heat of any liquid, giving it the capacity to absorb a large quantity of heat while changing only slightly in temperature.

► As a result, large lakes and other bodies of water tend to moderate the air temperature and the human body is better able to maintain a steady internal temperature under changing outside conditions.


► Water has an unusually high heat of vaporization (540 cal/g), it carries away a large amount of heat when it evaporates.

► Your body relies on the cooling effect of water evaporation.

► Most substances are more dense as solids than as liquids because molecules are more closely packed in the solid than in the liquid. Water, however, is different. Liquid water has a maximum density of 1.000 g/mL at 3.98°C but then becomes less dense as it cools. When it freezes, its density decreases still further to 0.917 g/mL. Ice floats on liquid water, and lakes and rivers freeze from the top down. If the reverse were true, fish would be killed in winter.


8.14 Solids

► There are many different kinds of solids. The most fundamental distinction between solids is that some are crystalline and some are amorphous.

► Crystalline solid: A solid whose atoms, molecules, or ions are rigidly held in an ordered arrangement. Crystalline solids can be further categorized as ionic, molecular, covalent network, or metallic.

► Amorphous solid: A solid whose particles do not have an orderly arrangement.


A summary of the different types of solids and their characteristics is given below.


8.15 Changes of State

► When a substance changes state, energy added is used to overcome attractive forces instead of increasing kinetic energy so temperature does not change.

► Heat of fusion: The quantity of heat required to completely melt a substance once it has reached its melting point.

► Heat of vaporization: The quantity of heat required to completely vaporize a substance once it has reached its boiling point.


A heating curve for water, showing the temperature and state changes that occur when heat is added.


Chapter Summary

►According to the kinetic–molecular theory of gases, the behavior of gases can be explained by assuming that they consist of particles moving rapidly at random, separated from other particles by great distances, and colliding without loss of energy.

►Boyle’s law says that the volume of a fixed amount of gas at constant temperature is inversely proportional to its pressure.

►Charles’s law says that the volume of a fixed amount of gas at constant pressure is directly proportional to its Kelvin temperature.


Chapter Summary Cont.

►Gay-Lussac’s law says that the pressure of a fixed amount of gas at constant volume is directly proportional to its Kelvin temperature.

►Avogadro’s law says that equal volumes of gases at the same temperature and pressure contain the same number of moles.

►The four gas laws together give the ideal gas law,PV = nRT, which relates the effects of temperature, pressure, volume, and molar amount.

►At 0°C and 1 atm pressure, called standard temperature and pressure (STP), 1 mol of any gas occupies a volume of 22.4 L.



►The pressure exerted by an individual gas in a mixture is called the partial pressure. Dalton’s law: the total pressure exerted by a mixture is equal to the sum of the partial pressures of the individual gases.

►There are three major types of intermolecular forces, which act to hold molecules near one another in solids and liquids. Dipole–dipole forces occur between polar molecules. London dispersion forces occur between all molecules as a result of temporary molecular polarities. Hydrogen bonding, the strongest of the three forces, occurs between a hydrogen atom bonded to O, N, or F and a nearby O, N, or F atom.



►Crystalline solids are those whose constituent particles have an ordered arrangement; amorphous solids lack internal order. There are several kinds of crystalline solids, ionic solids, molecular solids, covalent network solids, and metallic solids,.

►The amount of heat necessary to melt a given amount of solid at its melting point is its heat of fusion. Molecules escape from the surface of a liquid resulting in a vapor pressure of the liquid. At a liquid’s boiling point, its vapor pressure equals atmospheric pressure. The amount of heat necessary to vaporize a given amount of liquid at its boiling point is called its heat of vaporization.

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